Question

Find the value of $k$ for which the given system of equations has a unique solution:

$x-ky=2$;

$3x+2y=-5$

• A. $k\ne -\frac{2}{3}$
• B. $k\ne \frac{1}{2}$
• C. $k\ne \frac{3}{2}$
• D. $k\ne -\frac{5}{2}$

Answer 1

The correct option is A $k\ne -\frac{2}{3}$

The equations are
$x-ky-2=0$
$\Rightarrow a_1=1,b_1=-k,c_1=-2$
$3x+2y+5=0$
$\Rightarrow a_2=3,b_2=2,c_2=5$
The given system of equations has a unique solution
$\Rightarrow \frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
$\Rightarrow \frac{1}{3}\ne -\frac{k}{2}$
$\Rightarrow$$k\ne -\frac{2}{3}$